The 1990 Nobel Prize for Economics was awarded for work published in the 1950s on the "portfolio problem". The "portfolio problem" can be explained by considering two assets, A and B. Asset A has a particular risk and return associated with it. Asset B has a lower risk and a lower return. If an investor puts all his money into asset A he can expect the return and risk associated with the underlying asset. Similarly if he invests entirely in asset B he can expect the risk and return associated with that asset. However, what risk and return can be expected if he splits his investment between the two assets?
The return and risk of a portfolio containing both asset A and B is a function of the included assets but the relationship is not necessarily linear. In fact for most real world assets certain portfolios containing both asset A and asset B can exhibit a lower risk for a given return than either of the underlying assets. The benefit of this type of diversification follows from the fact that the financial performance of the two assets are not directly linked to each other and in general are imperfectly correlated. The optimal mix of asset A and asset B lies along a curve called the "efficient frontier". A methodology exists which can be used to compute the efficient frontier. The mathematics used to measure risk and return and to compute the frontier is discussed at length in numerous financial management textbooks, including Investments, authored by William F. Sharpe. However a brief explanation of the methods for measuring risk and return are useful to appreciate certain aspects of the present invention.
In general, each financial asset has an associated risk and a corresponding return which must be defined for purposes of computation. To compare two assets a standardized measure of risk and return must be developed. The texts define alpha, beta, market return and risk free return. Beta is a normalized measure of asset risk. An asset which "moves" exactly in proportion with the market has a beta of 1.0. An asset which moves only half as much as the market has a beta of 0.5. An asset which doesn't move at all has a beta of zero. Thus beta is a measure of the covariance of an asset's return compared with the market. Risk free return is the measure of return of a risk free investment such as U.S. treasury bills (beta=approximately 0.0). Return is defined as the percentage change in wealth over the holding period for the asset. Alpha is a measure of the amount by which the return on an asset exceeds the return of a market benchmark having the same level of risk as the asset. Many texts describe alpha as how "mispriced" an asset is. Values for alpha are expressed as a percent per time period.
It is well known that an "efficient" portfolio can be combined with a risk free investment to create an optimal portfolio at any defined level of risk. FIG. 1 sets forth these relationships in a graphical fashion.
An efficient portfolio calculator can compute the efficient frontier for a portfolio of assets if the expected future values of these parameters are known or estimated. However, these efficient frontier calculations are quite sensitive to the values of the expected return attributed to the assets, as well to their correlation or covariance.
For example, a problem directly associated with the conventional computation of optimal or efficient portfolios, is that an implicit choice is made between two assets having nearly identical risk but slightly differing returns. In this case, the classic computation will typically select the highest return asset only for inclusion in the portfolio, even though its expected return is not known with precision.
It is also important to note that traditional efficient frontier calculations ignore, or accommodate only in an indirect fashion, other differences among assets having similar return and covariance attributes. For example, the industry sector grouping, or investment style (e.g. growth versus value) of the assets is not directly considered in creating the portfolio. Using the traditional efficient frontier calculation, a portfolio could be selected which lacks appropriate industry sector or investment style diversification, and which ignores assets with excellent but slightly suboptimal average expected returns. All of these shortcomings are undesirable.
Thus a straightforward or obvious application of traditional portfolio theory to the selection of mutual funds to form properly risk-targeted, well-diversified investment portfolios is problematic.